My wife went to install and upgrade to El Capitan on her MacBook Pro from Yosemite and now is left with a botched install with the mac installer stuck in an endless install loop. No boot up or any sign of the previous OS. We have no Time Machine backup. No one's fault but my own.

In the case that the hard drive may be salvagable, I replaced it with another mac formatted HD. I have the original Mac OS X install DVD/CD disks cannot remember the startup procedure/Key presses to get the OS X disks to install the OS on the new Mac formatted HD. I've researched the internet and apple and cannot find any start up routine that will boot from the install disks.

The drive where the El Capitan install didn't finish may be OK. If you have an external drive enclosure or universal drive cable (what I use), you can try starting from that drive in Safe Mode: https://support.apple.com/en-us/HT201262

Here's the nifty Time Machine system I'm using:I bought two 2T mini drives from Other World Computing. They're the aluminum enclosure, but it probably doesn't matter. These drives are very quiet and spin up very quickly, so you probably won't even notice them.
I have them both attached and entered in Time Machine. Time Machine will automatically back up to one, then the other, and so on. That way I have two physical drives with full Time Machine backups.

"Design is not just what it looks like and feels like. Design is how it works."
Steve Jobs